Question

The pair of equations $3^{x+y}=81$ and ${81}^{x-y}=3$ has:

• A. No common solution
• B. The solution $x=2,y=2$
• C. The solution $x=2\frac{1}{2}$ , $y=1\frac{1}{2}$
• D. A common solution in positive and negative integers
• E. None of these

Answer 1

The correct option is E None of these

$3^{x+y}=81=3^4;\therefore x+y=4;{81}^{x-y}=3={81}^{\frac{1}{4}}\therefore x-y=\frac{1}{4}$
$\therefore x=2+\frac{1}{8},y=2-\frac{1}{8}$ and the correct choice is (e).